Unit 5: Rotational Motion

Introduction

Rotational kinematics describes motion around a fixed axis. It is analogous to linear kinematics, but instead of displacement, velocity, and acceleration, we use **angular displacement (θ), angular velocity (ω),** and **angular acceleration (α).**

Key Concepts

• Angular Displacement (θ): Measured in radians, represents the change in rotational position.
• Angular Velocity (ω): The rate of change of angular displacement (rad/s).
• Angular Acceleration (α): The rate of change of angular velocity (rad/s²).
• Direction: Counterclockwise is usually positive; clockwise is negative.

Mathematical Routines

• Angular kinematic equations (analogous to linear kinematics):
  • ω = ω₀ + αt
  • θ = ω₀t + ½ αt²
  • ω² = ω₀² + 2αθ
• Radians as the natural unit for angular displacement.
• Converting between degrees and radians: \(1 \text{ rad} = 57.3^\circ\).

Creating Representations

• Diagrams: Use circular motion diagrams with labeled angular displacement, velocity, and acceleration.
• Graphs: Plot θ vs. t, ω vs. t, and α vs. t to analyze motion.

Scientific Questioning & Argumentation

• Question: "What happens when α is zero?"
• Argumentation: No angular acceleration means constant ω, similar to constant velocity in linear motion.

Practice Activities

Summary & Exam Preparation Tips

• Use kinematic equations for angular motion just like in linear motion.
• Pay attention to sign conventions (counterclockwise = positive).